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Mar 16, 2011 at 0:21 comment added Marty I think you're right -- it's not so easy, and I'm not aware of a reference. This sort of question seems related to general questions along the line of "how do Bernstein components behave under isogeny?" I'll let you know if I think of anything...
Mar 15, 2011 at 20:44 comment added Kevin Buzzard Marty: it might not be so easy. I was in Oberwohlfach with Bushnell and Henniart last week and I asked them both. Colin seemed to think that this question might have been resolved relatively recently, but I can't remember if he gave a precise reference. I wondered whether someone else could fill me in on any details---what I'm saying is that an answer might well be of the form "see this recent paper" rather than "here's an example I just cooked up". Of course I could be wrong! PS you can just delete any answer you post here as far as I know---and then undelete it later if you feel like it!
Mar 15, 2011 at 19:07 comment added Marty I'll try to finish the answer later!
Mar 15, 2011 at 19:07 history edited Marty CC BY-SA 2.5
Drastic cut, and postponement of answer.
Mar 15, 2011 at 18:34 comment added Marty Aaahhhh! I clicked on post accidentally! How do I undo that... Now I really have to finish this answer!!
Mar 15, 2011 at 18:33 history answered Marty CC BY-SA 2.5